Introduction to computational algebraic statistics. (English) Zbl 1442.62765

Iohara, Kenji (ed.) et al., Two algebraic byways from differential equations: Gröbner bases and quivers. Cham: Springer. Algorithms Comput. Math. 28, 185-212 (2020).
Summary: In this paper, we introduce the fundamental notion of a Markov basis, which is one of the first connections between commutative algebra and statistics. The notion of a Markov basis is first introduced by P. Diaconis and B. Sturmfels [Ann. Stat. 26, No. 1, 363–397 (1998; Zbl 0952.62088)] for conditional testing problems on contingency tables by Markov chain Monte Carlo methods.
For the entire collection see [Zbl 1444.14002].


62R01 Algebraic statistics
62H17 Contingency tables
62-08 Computational methods for problems pertaining to statistics
65C05 Monte Carlo methods
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)


Zbl 0952.62088
Full Text: DOI arXiv


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